The formation of gas giants and ice giants by pebble accretion

Michiel LambrechtsAnders Johansen / Alessandro Morbidelli

Observatoire de la côte d’azurExoplanets in Lund 6-8 May 2015

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Planets and pebbles in protoplanetary discs

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HD100546, 2Msol,~5Myr.- 400 AU wide ppd- potential imaged gas giant planet at 53 AU (Quanz et al 2014)

50AU

Debes et al 2013 ALMA collaboration+, 2015

TW Hya ppd (~5Myr) [left]- 80 AU planet of 6-28 ME- ~180--300 Me in pebbles (Wilner+2005, bergin+2013)

HL tau ppd (~1Myr) [right]- formation of planets in a ~1Myr old disc- large pebble component (Greaves et al 2008)

(1) Planets form in protoplanetary discs (few Myr, in wide circular orbits, and in multiples)(2) Simultaneously, there is a large solid component in pebbles (mm-dm sized particles)

HL tau

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Pebble accretion dynamics 1

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Bondi pebble accretionLambrechts & Johansen, 2012

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- Hill regime starts above a transition mass:

- accretion occurs from the full Hill radius

- relative velocities are set by the Keplerian shear (independent of )

Pebble accretion dynamics 2

Mt ⇡ 3⇥ 10�3⇣ r

5AU

⌘3/4M�

Hill pebble accretionLambrechts & Johansen, 2012

4

4

- Hill regime starts above a transition mass:

- accretion occurs from the full Hill radius

- relative velocities are set by the Keplerian shear (independent of )

Pebble accretion dynamics 2

Mt ⇡ 3⇥ 10�3⇣ r

5AU

⌘3/4M�

Hill pebble accretionLambrechts & Johansen, 2012

4

4

Difference with planetesimals

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MMSN scaling

Mpeb ⇠ rHvH⌃peb

Mplan ⇠ r2accvH⇢plan

⇢plan ⇠ ⌃plan/hplan

hplan ⇠ vH/⌦K ⇠ rH

Mpeb ⇠ rHvH⌃peb

See also:Ormel & Klahr 2010

Rafikov 2004 planetesimals/fragmentsand Levison et al 2010

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An analytic “toy model”

+⌃p(r, t)Mc,p(r, t) ⇡2(⌧f/0.1)

2/3rHvH⌃p⌧f(r, t)

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Birnstiel et al, 2012

Lambrechts and Johansen, 2014

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Pebble drift planets

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- start with compact configuration of 4 embryos

- few Myr in disc with pebble surface density reduced by a factor ~5 with respect to MMSN

- inside out planet formation

- pebble flux filtering

17% for one core and about 50% for a ‘Solar System’

- mass budget: total mass: ~120-160 Me terrestrial mass: 50 Me/2 (inside the ice line)

f =Mc

MF=

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⇡

⇣ ⌧f0.1

⌘�1/3⌘�1

⇣rHr

⌘2

⇡ 0.034⇣ ⌧f0.1

⌘�1/3✓Mc

ME

◆2/3 ⇣ r

10AU

⌘�1/2

Lambrechts and Johansen, 2014

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- overcome type I migration ice giants form ~ in situ -> cross over mass

- steep initial dust-to-gas ratio dependency

Characteristics of the model

8 Bucchave et al, 2012

For more talk by Bert!

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Mc

Menv

Coregrowth

Envelopegrowth

Runawaygas accretion

�0.07 g/cm2, r=10 AU�pPebble accretion scenario

0 2 4 6 8 100

10

20

30

40

50

t /Myr

M/M

E

Core accretion with pebbles:

- rapid formation of the core without enhancements of the solid surface density

- faster contraction of the gaseous envelope, because of pebble isolation mass

- particular attention at forming ice giants

The core accretion scenariowith pebbles

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The critical core mass

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- Protoplanetary disc lifetimes constrain accretion rates to be high to complete cores

- critical core mass increase with accretion rate (Rafikov 2006)

- The high accretion rates necessary to form the cores lead to core masses much too large compared to the gas giants in the Solar System

- Therefore halting the accretion is a necessity in the core accretion scenario (or a lot of ice pollution)

Lambrechts et al 2014

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The pebble isolation mass

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- gravity of the core perturbs gas disc- creates a pressure bump (shallow gap) that traps particles outside the accretion radius, thereby halting solid accretion- pebble isolation mass ~ critical core mass

Mc

M iso

Menv

Coregrowth

Envelopecontraction

Runawaygas accretion

�p�0.07 g/cm2, r=10 AUPebble accretion scenario

0 2 40

10

20

30

40

50

t /Myr

M/M

E

Miso

⇡ 20⇣ r

5AU

⌘3/4

ME

/✓H

r

◆3

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Ice giant / gas giant divide

Lambrechts et al 2014

- radial and compositional dichotomy between gas and ice giants

- gas giants in the inner disc (<10 AU) reach isolation and therefore undergo runaway gas accretion

- ice giants have not undergone isolation (or only briefly). The blue lines show the least polluted envelope that can be bound to the core.

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Jupiter

Lambrechts et al 2014Lambrechts et al 2014

Saturn Uranus Neptune

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Exoplanets with envelopes

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H2

H2O

SiO2

10-1 100 101 102 103 104

100

101

M /ME

R/RE

Data from open exoplanets catalogue

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Expanding the scenario

• full disc models see following talk by Bertram Bitsch

• terrestrial embryo/planet formation(Guillot+2014, Johansen+2015, Morbidelli+2015, Levison/Kretke group+2015, Lambrechts in prep)

• (hybrid) N-body codesKretke & Levison, 2014, Levison+2015 , Chambers, 2014, and above

• doing the gas envelope contraction carefully Piso & Youdin 2014,

Mordasini+a,b 2014, Ormel, 201414

1. 2. 3.10-4 ME 0.01-10ME

Mc

M iso

Menv

Coregrowth

Envelopecontraction

Runawaygas accretion

�p�0.07 g/cm2, r=10 AUPebble accretion scenario

0 2 40

10

20

30

40

50

t /Myr

M/M

E

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Questions?

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Lambrechts & Johansen, 2014Lambrechts, Johansen, Morbidelli, 2014Lambrechts & Johansen, 2012Morbidelli, Lambrechts +, 2015 submittedBitsch, Lambrechts & Johansen, 2015 submitted

• formation in a few Myr

• halting solid accretion (~20 Me)form gas giants and ice giants

• dust-to-planet efficiency (~50%)

• metallicity correlation (steep)

• overcome type I migration

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